A method based on LS-SVM to estimate time-domain Green function
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A method based on LS‑SVM to estimate time‑domain Green function Jianwei Wang1,2 · Liping Sun2 · Yuqing Wang3 · Shaoshi Dai2 Received: 26 February 2020 / Accepted: 9 September 2020 © The Japan Society of Naval Architects and Ocean Engineers (JASNAOE) 2020
Abstract How to calculate the 3D time-domain Green function and its gradients accurately and efficiently is the key to solving the hydrodynamic problem of ships. In this paper, the least square support vector machine (LS-SVM) theory was proposed for the first time to solve the ordinary differential equations (ODEs) satisfied by the time-domain Green function and the spatial derivatives in time domain. Furthermore, the computational advantages of the theory were discussed from three perspectives which were the accuracy, stability and rapidity of the calculation of the time-domain Green function. This approach was validated by comparing the obtained results with those of alternative methods which was found to effectively improve the accuracy and stability of calculation of the time-domain Green function and the spatial derivative. Keywords The time-domain green function · LS-SVM · ODE · Hydrodynamics
1 Introduction Accurate prediction of wave-induced responses and loads are a key link in the design of ships and Marine structures. There are two main methods that are the frequency-domain one [1] and the time-domain one [2]. Compared with the frequency-domain method, the time-domain method can solve the instantaneous motion response [3] and nonlinear largeamplitude motion [4] problems of ship or Marine structures interacting with waves. When the three-dimensional timedomain method is applied to solve the hydrodynamic problem, the estimation of the time-domain Green function is involved. In recent years, the wave load analysis in time domain is urgently needed in ship design purpose, which is based on the potential flow theory. Whether the program is developed with the so-called hybrid method [5–9], or the direct timedomain Green function method [10–13], three-dimensional * Jianwei Wang [email protected] 1
School of Mechanical Engineering, Yanshan University, Qinhuangdao 066000, Hebei, China
2
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, China
3
College of Mathematics and Information Science and Technology, Hebei Normal University of Science and Technology, Qinhuangdao 066000, Hebei, China
time-domain Green function plays a crucial role in solving the hydrodynamic problems by the use of panel method [2]. However, considering that three-dimensional time-domain Green function involves an integral with an oscillating kernel over an infinite range and exhibits a high-frequency oscillatory behavior, and that amplitude increases with time increment, it is rather difficult to estimate the time-domain Green function directly and the major part of CPU time spent on computations. For instance, Newman [14], Beck and Liapis [3], and Lin and Yue [15] divided the computational domain of the
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